Find the Rank Dependent Utility and the Certainty Equivalent of the lottery (80,) under g(p) = p2 and u(x) = x.
1) Find the Rank Dependent Utility and the Certainty Equivalent of the lottery (80,) under g(p) = p2 and u(x) = x.
2) RDU as a better descriptive model: Start with the famous Allais Paradox of
01) and (5 89). Let
u(0) = 0. Show that under EU, one would get .11u(1m) > .10u(5m) and .11(1m) < .10u(5m) respectively, which cannot hold simultaneously. Next, show that under RDU with g(p) = p2, show that these two conditions become and . Show that these two conditions could
hold simultaneuosly as ..
3) Independence Axiom and Reduction of Compound Lotteries:Suppose the decision-maker is indifferent between two lotteries L1 = {10,.5;0,.5} and L2 = {4,1}. Show that under the independence axiom she should also be indifferent between L1 and {10,.25;4,.5;0,.25}. (Hint: Start with L1 ∼ L2, then using the independence axiom mix .5 proportion of both sides with .5 proportion of L1. What do you get?)
√
4) Assume that S = {s1,s2,s3}, u(x) = x, W(s1) = W(s2) = W(s3) = 0.4, and W(s1,s2) = W(s1,s3) = W(s2,s3) = 0.6. Calculate the RDU value of the prospect (1,s1;0,s2;9,s3).
